Tensor decompositions for multi-modal Big Data analytics

Low-rank matrix decompositions are a ubiquitous mathematical tool for data analysis. Unfortunately, they are intrinsically limited to 2-mode data. For this reason, tensor decompositions that generalize low-rank matrix decompositions to multi-modal data, are gaining importance in several fields, such as machine learning, neuroscience, scientific computing, and signal processing. This project focuses on the analysis of the geometry of additive tensor decompositions and will develop new geometry-exploiting algorithms for their computation.

Keywords:tensor decomposition, data analysis, Riemannian optimization

Disciplines:Algebraic geometry, Differential geometry, Mathematical software, Numerical analysis, Numerical computation, Data mining, High performance computing